25 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| Full Idea: We are able to reason about inconsistent beliefs, stories, and theories in useful and important ways | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| Full Idea: Do not multiply entities beyond necessity. | |
| From: William of Ockham (works [1335]) | |
| A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| Full Idea: Intuitionist logic appears most attractive in the form of a natural deduction system. | |
| From: Edwin D. Mares (Negation [2014], 5.5) |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| Full Idea: In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation. | |
| From: Edwin D. Mares (Negation [2014], 5.5) | |
| A reaction: How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome. |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| Full Idea: One reason for wanting a three-valued logic is to act as a basis of a theory of presupposition. | |
| From: Edwin D. Mares (Negation [2014], 3.1) | |
| A reaction: [He cites Strawson 1950] The point is that you can get a result when the presupposition does not apply, as in talk of the 'present King of France'. |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| Full Idea: The problem with material implication, and classical logic more generally, is that it considers only the truth value of formulas in deciding whether to make an implication stand between them. It ignores everything else. | |
| From: Edwin D. Mares (Negation [2014], 7.1) | |
| A reaction: The obvious problem case is conditionals, and relevance is an obvious extra principle that comes to mind. |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| Full Idea: Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction. | |
| From: Edwin D. Mares (Negation [2014], 2.2) | |
| A reaction: Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool. |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| Full Idea: On its standard reading, excluded middle tells us that bivalence holds. To reject excluded middle, we must reject either non-contradiction, or ¬(A∧B) ↔ (¬A∨¬B) [De Morgan 3], or the principle of double negation. All have been tried. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| Full Idea: If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false. | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: Mates's point is to show that passively taking the normal account of negation for granted has important implications. |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| Full Idea: In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning). | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: [compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating. |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| Full Idea: Many-valued logics do not have reasonable natural deduction systems. | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| Full Idea: Situation semantics for logics consider not what is true in worlds, but what information is contained in situations. | |
| From: Edwin D. Mares (Negation [2014], 6.2) | |
| A reaction: Since many theoretical physicists seem to think that 'information' might be the most basic concept of a natural ontology, this proposal is obviously rather appealing. Barwise and Perry are the authors of the theory. |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| Full Idea: The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| Full Idea: For the intuitionist, talk of mathematical objects is rather misleading. For them, there really isn't anything that we should call the natural numbers, but instead there is counting. What intuitionists study are processes, such as counting and collecting. | |
| From: Edwin D. Mares (Negation [2014], 5.1) | |
| A reaction: That is the first time I have seen mathematical intuitionism described in a way that made it seem attractive. One might compare it to a metaphysics based on processes. Apparently intuitionists struggle with infinite sets and real numbers. |
| 22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
| Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals. | |
| From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056 | |
| A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist. |
| 15959 | If the substantial form of brass implies its stability, how can it melt and remain brass? [Alexander,P] |
| Full Idea: If we account for the stability of a piece of brass by reference to the substantial form of brass, then it is mysterious how it can be melted and yet remain brass. | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 02.3) | |
| A reaction: [Alexander is discussing Boyle] |
| 15956 | The peripatetics treated forms and real qualities as independent of matter, and non-material [Alexander,P] |
| Full Idea: The peripatetic philosophers, in spite of their disagreements, all treated forms and real qualities as independent of matter and not to be understood in material terms. | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 54) | |
| A reaction: This is the simple reason why hylomorphism became totally discredited, in the face of the 'mechanical philosophy'. But there must be a physical version of hylomorphism, and I don't think Aristotle himself would reject it. |
| 15975 | Can the qualities of a body be split into two groups, where the smaller explains the larger? [Alexander,P] |
| Full Idea: Is there any way of separating the qualities that bodies appear to have into two groups, one as small as possible and the other as large as possible, such that the smaller group can plausibly be used to explain the larger? | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 5.02) | |
| A reaction: Alexander implies that this is a question Locke asked himself. This is pretty close to what I take to be the main question for essentialism, though I am cautious about couching it in terms of groups of qualities. I think this was Aristotle's question. |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| Full Idea: In 'situation semantics' individuals, properties, facts, and events are treated as abstractions from situations. | |
| From: Edwin D. Mares (Negation [2014], 6.1) | |
| A reaction: [Barwise and Perry 1983 are cited] Since I take the process of abstraction to be basic to thought, I am delighted to learn that someone has developed a formal theory based on it. I am immediately sympathetic to situation semantics. |
| 15963 | Science has been partly motivated by the belief that the universe is run by God's laws [Alexander,P] |
| Full Idea: The idea of a designed universe has not been utterly irrelevant to the scientific project; it is one of the beliefs that can give a scientist the faith that there are laws, waiting to be discovered, that govern all phenomena. | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 03.3) | |
| A reaction: Of course if you start out looking for the 'laws of God' that is probably what you will discover. Natural selection strikes me as significant, because it shows no sign of being a procedure appropriate to a benevolent god. |
| 15951 | Alchemists tried to separate out essences, which influenced later chemistry [Alexander,P] |
| Full Idea: The alchemists sought the separation of the 'pure essences' of substances from unwanted impurities. This last goal was of great importance for the development of modern chemistry at the hands of Boyle and his successors. | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 01.1) | |
| A reaction: In a nutshell this gives us the reason why essences are so important, and also why they became discredited. Time for a clear modern rethink. |
| 15981 | Absolute space either provides locations, or exists but lacks 'marks' for locations [Alexander,P] |
| Full Idea: There are two conceptions of absolute space. In the first, empty space is independent of objects but provides a frame of reference so an object has a location. ..In the second space exists independently, but has no 'marks' into which objects can be put. | |
| From: Peter Alexander (Ideas, Qualities and Corpuscles [1985], 6) | |
| A reaction: He says that Locke seems to reject the first one, but accept the second one. |
| 19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
| Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist. | |
| From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
| A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all. |
| 8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
| Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam. | |
| From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
| A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc. |
| 16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
| Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location. | |
| From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 |